Abstract We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. show that any compact solution whose second fundamental form satisfies a certain natural pinching condition must be family shrinking spheres. Andrews and Baker (J Differ Geom 85(3):357–395, 2010) have shown initial submanifolds satisfying this condition, ...

Using a mixture of analytic and numerical techniques we show that the mode-locked regions of quasi-periodically forced Arnold circle maps form complicated sets in parameter space. These sets are characterized by ‘pinched-off’ regions, where the width of the mode-locked region becomes very small. By considering general quasi-periodically forced circle maps we show that this pinching occurs in a ...

Some authors suggest that the pudendal nerve might be pinched against the pubic arc because of the forward tilting of the body on the bicycle seat (Ricchiuti 1999). Another explanation could be that the seat of the bicycle compresses the blood supply to the penis (Sommer et al. 2001). Penile blood pressure and blood flow can be measured via spectroscopy, Doppler ultrasound, penile transcutaneou...

ABSTRACT. In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, Lp-inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can ...

Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ : M \ Σ → H with prescribed singularities along Σ. When M = R, and H = H C , the complex hyperbolic space, this result has applications to the problem of ...

A classical theorem due to M. Berger [2] and W. Klingenberg [11] states that a simply connected Riemannian manifold whose sectional curvatures all lie in the interval [1, 4] is either isometric to a symmetric space or homeomorphic to Sn (see also [12], Theorems 2.8.7 and 2.8.10). In this paper, we provide a classification, up to diffeomorphism, of all Riemannian manifolds whose sectional curvat...

By means of an example it is shown that a supercritical bifurcation of an invariant 2-torus into an invariant 3-torus prevailing in the case of nonresonance may be replaced by a transcritical bifurcation into a pinched invariant 3-torus in the case of resonance. The connections of these bifurcation phenomena with the properties of the spectrum of the underlying invariant 2-torus are discussed. ...

In this study, neural cell sorting of high throughput and high purity is made using two-step separation by combining soft inertial microfluidics and pinched flow fractionation. Both finite element analysis tool and equivalent electric circuits modeling were used to design the microfluidic devices. Separation between neurons and glia cells from rat’s spine cord was demonstrated. To minimize the ...

A capillary plasma z-pinch as an alternative active medium of soft X-Ray lasers was studied experimentally and theoretically. The theoretical analysis was based on the self consistent solution of the so called “snow plow” model. The dynamics of pinched plasma is determined by the capillary parameters and by the time dependence of electrical current passing through it. The current time dependenc...